Another story about explaining how we surveyors think.
This one involves a simple one acre of land. I have tried explaining that a piece of land that measures 210 feet by 210 feet square is actually 1.01 acre, and one acre of land actually measures 208.71 feet square. Responses to that have varied from quizzical looks to incredulous looks. Why, everyone knows that an acre of land is "70 steps" on all sides!
My dookey storm started with "simple" geometry. A client's deed stated that his land measured 210 by 210 and contained one acre, "more or less." I think the original scrivener was on to something. The deed description said ""north along the road right-of-way" 210 feet, thence west 210, thence "south parallel to the road right-of-way" 210 feet, thence east 210 feet to close out. However, the road right-of-way was not going North, but at a pretty good angle from north. The parcel was a parallelogram, and even though the sides measured 210 by 210, the acreage calculated 0.85 acre. That was going to be the "more or less" the scrivener was referring to.
Any fool knows that one acre of land measured 210 by 210. It's carved into stone. I tried explaining geometry and that the area of a rectangle or square is base times height. But that only works when height is perpendicular to base. In the case of a parallelogram, the area is still base times height, but height is shorter when you calculate its length perpendicular to the base. I used a roll-up tape to prove to him that the existing pins that I had found measured 210 between all of them. I was not going to tell him that the distances were within a few hundredths of a foot from 210 feet. I had unsuccessfully tried in the past to explain decimal feet to someone like this person and decided not do that.
He had bought an acre of land and my survey was wrong according to him. I lost that survey to hard-headedness.
Lessons learned: Don't talk like a rocket scientist and use words like "parallelogram," "perpendicular," and "geometry." And phrases like "rectangular area is at a maximum when the angles are right angles." And terms like "right angle." Of course they are right! How could it be wrong? And how about units of measure that say "feet square" and "square feet?" One is a measure of length and the other is a measure of area, like an acre of land measures 210 feet square and contains an area of 43,560 square feet. I made my college class students think hard with questions like that on homework assignments. Watch the units of measure. What is an acre of land measured in chains? About 3.16 chains square and an area of one square chain, not 0.99999688 square chains. We had to work on significant figures and rounding off, too.
I once worked on a boundary for a large (1200 acre) golf course and development area in an extremely rural area. The subject property had several privately owned smaller tracts abutting it and creating an irregular boundary. It was interesting in the fact the owners were sparing no expense to quiet title and properly "fix" their boundary before the big development money started flowing.
One of the "less and except" parcels was a cemetery that had been around since before statehood. If I can remember correctly the description stated the property was "twelve and a half rods square, being one acre". 12.5 rods is 206.25', not 208.71'.
It was a good exercise in dealing with title examiners, attorneys and bankers. What made it more interesting was the fact the ancient native sandstone fence surrounding the cemetery measured real close to 209' square.
The development company eventually quit-claimed everything from the rock wall inward, as per my survey. It worked out to an amicable end, but the ambiguous description made dealing with everyone involved difficult.
If "road north" was the basis of bearings, I'm wondering how they ended up with something closer to true west, etc. for the other sides. Why wasn't the parcel originally as close to square as they could make it?
My explanation would have been to draw a parallelogram with about a 5 degree angle and 210 ft sides and ask them if that had the same area as their parcel or as a square.
It's been years, and I don't remember the state, but I heard, that in one state it was codified that 210 by 210' was an acre, at least at one time.
In Massachusetts, the State Environmental Code regulating septic systems, since about 1994, defines an acre as:
"a unit of land measure equal to 40,000 square feet which is considered a building acre in accordance with standard real estate practice."
When the deed says that 210ft x 210ft is an acre, I quote it as "called one acre".
I come across many deeds calling boundaries to be 210ft, 75varas, 70yards, 208.71ft and 208.72ft for one acre tracts.
We have areas where we quote to certain decimal places and in rural areas it is often only one.
In highly populated areas it is necessary to also quote the square feet.
I would've missed your homework assignment. I thought that ten chains square defined an acre, which is where the 43,560 sq ft came from, or 660 x66 feet.
BTW, EVERYBODY in the country knows that 210 x 210 is an acre. unfortunately.
City acres are less than that.
I get what you are saying and have no disagreement, but I would add that 210x210 feet is "an acre" when you consider the precision that the term "an acre" conveys.
Fascinating. If I've read this correctly, Harold is using the term "3.16 chains square" to represent a square with each side measuring 3.16 chains. J.T. is using the term "ten chains square" to represent an area of 10 square chains.
Certainly, J.T.'s rectangular plot that is 10 chains by 1 chain is 10 square chains, which is 43,560 square feet, or feet-squared as the physicists would say. And Harold's square plot that is 3.16 chains by 3.16 chains is 9.9856 square chains, or 43,497 square feet, which differs from J.T.'s only because of rounding.
No wonder folks weak in math have problems with this stuff.
This is why I like to hire new grads with philosophy rather than surveying degrees...sooner or later everything ends up as another ontology versus epistemology debate 😉
Plus there is the whole "Mississippi" factor to deal with
The best way to explain to someone about the area of a parallelogram is to take a 6 foot folding ruler. Make 4 of the sections into a square. Then gradually turn it into a parallelogram and keep going until there is practically no inside area.
The history of the Gunter's chain is interesting. From one source, it is based on the English unit of "4" and the number "10".
I "Googled" a few websites including Wikipedia for some numbers:
"unit square" will be the length of one side of a square.
"square units" will be a measurement of area.
one furlong = 660 feet = 10 chains.
one acre of land = 66 feet by 660 feet like J. T. says, in the shape of a rectangle.
one acre of land = 1 chain by 10 chains.
one acre of land = 4 perches by 40 perches or 4 rods by 40 rods.
one acre may have also been understood as an approximation of the amount of land a yoke of oxen could plough in one day which was rectangular and one "furrow" long (furlong).
one acre of land = about 3.16 chains per side in the shape of a square. working backwards, the square root of 43,560 square feet per acre is 208.71 feet square, and divided by 66 = 3.1623 chains square, or about 3.16 chains to the nearest link.
one chain square = 4,356 square feet = 1/10 of an acre.
one acre = 10 square chains = 43,560 square feet = 160 square rods.
one acre measures 12 rods and about 16 links per side. (12.6491 rods)(0.6941 rod x 25 links per rod = 16.22 links, or about 16 links).
ten acres = 10 chains square = 100 square chains = 660 feet square.
one chain = 4 rods = 4 poles = 4 perches = 100 links = 1/10 furlong.
one rod = 25 links = 16.5 feet
an old English furlong is 660 feet = 10 chains.
one chain = 1/10 furlong.
an old traditional acre of land is one chain by one furlong.
one acre of land = 160 perches (a perch was also used as a unit of area).
one perch = one square rod
an old Roman mile was 5000 feet long = 1000 paces (two steps) which was established by the consistent marching of a battalion of Roman soldiers. The English furlong did not fit the Roman mile, so the length of a mile was changed to 8 furlongs, or 5,280 feet.
the visual representation of an acre of land is about 9/10 the size of the standard American football field without the end zones.
one mile = 80 chains by 80 chains square or 6,400 square chains. Since one acre is 10 square chains, then one square mile is 6,400/10 = 640 acres.
1/4 section of land = 1/2 mile by 1/2 mile square = 160 acres = 160 rods square = 40 chains square = 1,600 square chains. And since one acre is 10 square chains, then 1/4 section of land is 1,600/10 = 160 acres.
There is a rhyme and reason to a Gunter's chain being 66 feet long with 100 links. The above numbers give pause for us to think about our predecessors and why they did what they did. Most of the mathematics were done in their heads, or with a piece of coal on the back of a shovel. They had to have a method using numbers and units of measurement that were easy to manipulate. Think of our unit of measurement of one foot having 12 sub-units of measurement in inches - it is not base 10 and difficult to use in calculations. One chain has 100 links and can be used as a decimal system, much like our current use of the decimal foot for linear measurements.
So, be careful when using calculators - those 7 or 8 decimal places of accuracy may not be a realistic representation of the accuracy obtained or the accuracy of the original numbers used in the calculations. Math Teacher made a good point: according to my calculations, the square root of 43,560 square feet is 208.7103256 feet and then dividing by 66 = 3.1622777 chains and squaring we get 10.0000000 square chains by not using any rounding off numbers. Math teacher used my example of about 3.16 chains exactly, and squaring to get 9.9856 square chains. The difference was in the rounding.
My hat's off to the old guys who dreamt up this system of measurements. It is what it is! B-)
And, as our Beerlegers from down under will undoubtably be aware as they watch Australia and New Zealand vie for the World Cup tomorrow, one chain is the distance between the wickets on a cricket pitch.
The same folks who define the acre as 210 by 210 also believe it is a unit of length.
"I want it an acre wide and two acres deep". If you give them anything but 210 by 420, you've got a lot of explaining to do. However, you've still got to explain the 2.02 acres on the plat, but they usually don't look at the plat anyway, they wad it up and stick it in their pocket, after you've been so careful to do a neat job.
Yep. all that nice drafting work is usually for my eyes only.
Oh, and I have learned to round off for some folks - 210 X 420 = 2.0 acres. B-)
the pickets on a cricket's witch.....wait, what?!?!:-P
Yep. Perfect example.
In our little rural area 210x210 is also known as a "country acre". I guess the old timers could remember that easier than 208.71x208.71. It was also easier to figure in your head when measuring off that "acre" that Aunt Selma gave Cousin Ed by "steppin it off" from that big old oak tree near the horse pasture. Angles different than 90° have always caused that glazed over look in the eyes of Cousin Ed's son in law that surveyed one summer and knows about measurin off land. I've seen recorded deeds that described measurements as 70 "average steps to the common man". Good times, for sure!
I was quite surprised at the size of an acre.
To plough an acre with with a 9 inch split, a man and his horse would need to walk 16 miles per day.
No 9 to 5 jobs in those days.
Funny this topic is currently being discussed. I just had a discussion with an adjoiner today about this, and he asked me about an acre being 210 by 210.
